Poststack layer replacement
Now consider another practical application of wave-equation datuming to 2-D surface seismic data — removing the degrading effect of an irregular water-bottom topography on the continuity and geometry of reflections below. This problem is particularly severe in areas with a strong velocity contrast between the water layer and the substratum. Despite the usual 3-D nature of the problem, the 2-D interpretation of the target reflections often can be improved by replacing the velocity of the water layer with the velocity of the substratum.
Consider the zero-offset section shown in Figure 8.1-3a based on the velocity-depth model shown in Figure 8.1-1a. Poststack layer replacement involves two extrapolation steps:
- The first step in poststack layer replacement involves downward continuing the wavefield at the surface (Figure 8.1-3a) to the water bottom (horizon 2 in Figure 8.1-1a) using the water velocity in extrapolation. The intermediate result is shown in Figure 8.1-3b. Note that in this horizon-flattened section, the water-bottom reflection is at t = 0, which means that all receivers are situated on the irregular water bottom. If we specified the overburden velocity or the water-bottom topography incorrectly, then the water-bottom reflection would not be at t = 0. In this respect, the intermediate section becomes a useful diagnostic tool before moving to the next step. In fact, wave-equation datuming actually can be applied layer by layer for structural model restoration. At each layer boundary, by examining the flatness of the event at t = 0 and observing any arrival-time departures of the event from t = 0, the validity of an estimated velocity-depth model can be verified.
- The second step in poststack layer replacement involves upward continuation of the intermediate wavefield (Figure 8.1-3b) back to the surface z = 0 using the velocity of the substratum (2000 m/s). Figure 8.1-3c is the zero-offset section at z = 0 after layer replacement.
Figure 8.1-3 Poststack layer replacement involves two steps. Step 1: The zero-offset section (a) is extrapolated down to the water bottom (horizon 2 in Figure 8.1-1a) using the water velocity. Section (b) is obtained when the receivers are placed along the water bottom. Step 2: This intermediate wavefield is extrapolated back up to the surface using the velocity of the stratum below the water bottom (2000 m/s). The resulting zero-offset section (c) can be compared against the zero-offset section derived independently (d) using the same velocity-depth model as in Figure 8.1-1a, except the overburden velocity is the same as that of the substratum (2000 m/s) as shown in Figure 8.1-1b.
A zero-offset section was created from the same velocity-depth model (Figure 8.1-1a) as for Figure 8.1-3a, except that the first layer velocity was set to 2000 m/s (Figure 8.1-1b). Compare this zero-offset section as shown in Figure 8.1-3d with the output of layer replacement as shown in Figure 8.1-3c, and note that the two sections are largely equivalent. Both layer replacement and depth migration are processes aimed at removing the effects of the complex overburden. However, note that layer replacement only requires accurate representation of the overburden (horizon 2 in Figure 8.1-1a), while depth migration requires accurate representation of the entire velocity-depth model (Figure 8.1-1a). Also note that the output from depth migration is a migrated depth section, while the output from layer replacement is an unmigrated time section (Figure 8.1-3c). After eliminating the complex overburden effect, this section only requires time migration.